Exotic orientations for homogeneous spaces

Andrew Baker (University of Glasgow)

Monday 8th January 16:00-17:00 Maths 311B

Abstract

Orientability for (connected, compact, closed) smooth manifolds is a very basic notion leading to such phenomena as Poincaré duality. The origins of this lie in orientations for vector bundles, in turn controlled by a topological invariant called the first Stiefel-Whitney class and giving rise to Thom isomorphisms.

All of this can be generalised to multiplicative cohomology theories and I will review the basic ideas. The first really interesting exotic examples involve K-theory, spinors and Clifford algebras; more recently string orientations for topological modular forms have been heavily studied.

A useful class of examples is provided by homogeneous spaces, i.e., quotients of compact Lie groups by closed subgroups. Identifying when these have K-theory orientations or TMF-orientations involves calculations some of which reduce to standard Lie theory.

Add to your calendar

Download event information as iCalendar file (only this event)